Exchange symmetry contributions

SUperSYmmetry A symmetry-like relation between two dissimilar systems that comes from a symmetry of mathematical expressions that describe them. Triple-Exchange A contribution to the exchange interaction (valence repulsion of molecules) non-additivity effect coming from a single electron-exchange between two molecules by mediation of a third one. 

Reorientations produce characteristic maxima in the relaxation rate, which may be different for the various symmetry species of CD4. The measured relaxation rates exhibit dependence on two time constants at low temperatures, but also double maxima for both relaxation rates. We assume that molecules may move over some places (adsorption sites) on the cage walls and experience different local potentials. Under the assumption of large tunnelling splittings the T and (A+E) sub-systems relax at different rates. In the first step of calculation the effect of exchange between the different places was considered. Comparison with experimental data led to the conclusion that we have to include also a new relaxation process, namely the contribution from an external electric field gradient. It is finally quite understandable to expect that such effect appears when CD4 moves in the vicinity of a Na+ ion. 

As noted above at higher densities the EoS is sensitive to 3NF contributions. Whereas the 3NF for low densities seems now well understood its contribution to nuclear matter densities remains unsettled. In practice in calculations of the symmetry energy in the BHF approach two types of 3NF have been used in calculations in ref.[4] the microscopic 3NF based upon meson exchange by Grange et al. was used, and in ref. [15] as well in most VCS calculations the Urbana interaction. The latter has in addition to an attractive microscopic two-pion exchange part a repulsive phenomenological part constructed in such a way that the empirical saturation point for SNM is reproduced. Also in practice in the BHF approach to simplify the computational efforts the 3NF is reduced to a density dependent two-body force by averaging over the position of the third particle. 

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

The ratio of symmetry numbers s s° in equation 11.40 merely represents the relative probabilities of forming symmetrical and unsymmetrical molecules, and ni and nf are the masses of exchanging molecules (the translational contribution to the partition function ratio is at all T equal to the power ratio of the inverse molecular weight). Denoting as AX, the vibrational frequency shift from isotopically heavy to light molecules (i.e., AX, = X° — X ) and assuming AX, to be intrinsically positive, equation 11.40 can be transated into... 

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